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Hi!

I want to find the Fourier transform of

[tex] \int_{-\infty}^t f(s-t)g(s) ds [/tex].

The FT

[tex] \int_{-\infty}^t h(s) ds \rightarrow H(\omega)/i\omega + \pi H(0) \delta(\omega)[/tex]

is found in lots of textbooks. So if I let h(s) = f(s-t)g(s), I need to find the FT of h(s)

[tex] H(\omega) = \int_{-\infty}^{\infty} h(s) \frac{e^{-i\omega s}}{\sqrt(2\pi)}ds = \int_{-\infty}^{\infty} f(s-t)g(s) \frac{e^{-i\omega s}}{\sqrt(2\pi)} ds [/tex].

But there I'm stumped, what can I do? I can do FT of products like f(s)g(s), but this isn't exactly like that.

I want to find the Fourier transform of

[tex] \int_{-\infty}^t f(s-t)g(s) ds [/tex].

The FT

[tex] \int_{-\infty}^t h(s) ds \rightarrow H(\omega)/i\omega + \pi H(0) \delta(\omega)[/tex]

is found in lots of textbooks. So if I let h(s) = f(s-t)g(s), I need to find the FT of h(s)

[tex] H(\omega) = \int_{-\infty}^{\infty} h(s) \frac{e^{-i\omega s}}{\sqrt(2\pi)}ds = \int_{-\infty}^{\infty} f(s-t)g(s) \frac{e^{-i\omega s}}{\sqrt(2\pi)} ds [/tex].

But there I'm stumped, what can I do? I can do FT of products like f(s)g(s), but this isn't exactly like that.

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